The coronavirus spike protein, the key entity effectuating membrane fusion, cannot exist without membrane-active fragments. In addition to fusion peptides, among such domains are HR1 and HR2. Crucial to the spike's refolding and membrane fusion, they are believed to both interact with each other and bind to the membranes that are merged. To elucidate HR2's precise role in this process, an understanding of its structure and behaviour is required. Here, we used various computational approaches to study SARS-CoV-2 spike HR2's (1163-1211) interaction with membranes in the context within which it operates in live spike. During simulations with model bilayers, HR2 remained hugely unresponsive to the presence of a membrane, however, when extended to include the transmembrane domain (TMD) (1212-1234) and/or membrane-active preHR2 fragment (1147-1161), HR2's binding to model bilayers was markedly enhanced. The trimeric coiled-coil of HR2 does not dissociate either on its own or with added TMD and/or preHR2. Molecular hydrophobicity potential (MHP) mapping showed that HR2's central part possesses a tilted oblique-oriented motif characteristic of "textbook" membrane-active peptides, albeit flanked by highly hydrophilic fragments. A truncated HR2 only encompassing this motif had a greater affinity for membranes, suggesting HR2 has a modular structure with a membrane-active segment masked by flanking regions and might be potentiated by HR2-adjacent domains and other factors coming into play after the spike gets enzymatically cleaved. Such a modular structure may have evolved for HR2's membrane activity to be regulated very subtly and "switched on" at precisely the right moment during viral fusion.